The main way to understand what rights, if any, a non-human animal has is to ask what its moral status is. It’s tempting to think that moral status is something that you either have or you don’t. Thinking along these lines usually means saying that only humans are moral beings that have rights, and everything else doesn’t.
But we often make distinctions between greater and lesser moral status.
This shows that there is something in between having full moral status, and none at all.
Hopefully this helps us understand our current topic better. Non-human animals might not be granted the same moral status as humans, but they could still have more than an inanimate object.
If this is a good reason, then we have certain obligations to animals. This doesn’t seem to entail that we are obliged not to kill them, only that we are obliged to not cause them undue pain or suffering.
Basing animals' moral status on their ability to feel pain is most closely associated with consequentialist ethics. That’s because it often finds things such as pleasure and pain directly relevant ethical considerations.
Even though consequentialism seems most suited to take animal rights seriously, other positions can accommodate them as well. Although deontology and character ethics focus on human concerns, animals can be ethically important insofar as our actions towards them tell us something about ourselves.
There are other reasons to think that we might have responsibilities to non-human animals. For instance, there is the idea that we're entrusted with the care of certain things. And this could include animals in general, endangered species in particular, and the environment more broadly.
But you might be asking: why should we be caretakers? It’s a bit clearer in a religious context. If God created nature, then God entrusts it to us and we would be responsible for taking care of it in the meantime.
This can be translated into a secular context.
Although it is only indirect, there is still a strong sense of responsibly towards animals.
Source: Sheep image, public domain, http://bit.ly/2bcgOhn